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Accuracy verification methods : theory and algorithms / / Olli Mali, Pekka Neittaanmaki, Sergey Repin
| Accuracy verification methods : theory and algorithms / / Olli Mali, Pekka Neittaanmaki, Sergey Repin |
| Autore | Mali Olli |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Dordrecht, Netherlands : , : Springer, , 2014 |
| Descrizione fisica | 1 online resource (xiii, 355 pages) : illustrations |
| Disciplina | 366 |
| Collana | Computational Methods in Applied Sciences |
| Soggetto topico |
Numerical calculations - Verification
Mathematical models |
| ISBN | 94-007-7581-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Errors Arising In Computer Simulation Methods -- 1.1 General scheme -- 1.2 Errors of mathematical models -- 1.3 Approximation errors -- 1.4 Numerical errors -- 2 Error Indicators -- 2.1 Error indicators and adaptive numerical methods -- 2.1.1 Error indicators for FEM solutions -- 2.1.2 Accuracy of error indicators -- 2.2 Error indicators for the energy norm -- 2.2.1 Error indicators based on interpolation estimates -- 2.2.2 Error indicators based on approximation of the error functional -- 2.2.3 Error indicators of the Runge type -- 2.3 Error indicators for goal-oriented quantities -- 2.3.1 Error indicators relying on the superconvergence of averaged fluxes in the primal and adjoint problems -- 2.3.2 Error indicators using the superconvergence of approximations in the primal problem -- 2.3.3 Error indicators based on partial equilibration of fluxes in the original problem -- 3 Guaranteed Error Bounds I -- 3.1 Ordinary differential equations -- 3.1.1 Derivation of guaranteed error bounds -- 3.1.2 Computation of error bounds -- 3.2 Partial differential equations -- 3.2.1 Maximal deviation from the exact solution -- 3.2.2 Minimal deviation from the exact solution -- 3.2.3 Particular cases -- 3.2.4 Problems with mixed boundary conditions -- 3.2.5 Estimates of global constants entering the majorant -- 3.2.6 Error majorants based on Poincar´e inequalities -- 3.2.7 Estimates with partially equilibrated fluxes -- 3.3 Error control algorithms -- 3.3.1 Global minimization of the majorant -- 3.3.2 Getting an error bound by local procedures -- 3.4 Indicators based on error majorants -- 3.5 Applications to adaptive methods -- 3.6 Combined (primal-dual) error norms and the majorant -- 4 Guaranteed Error Bounds II -- 4.1 Linear elasticity -- 4.1.1 Introduction -- 4.1.2 Euler–Bernoulli beam -- 4.1.3 The Kirchhoff–Love arch model -- 4.1.4 The Kirchhoff–Love plate -- 4.1.5 The Reissner–Mindlin plate -- 4.1.6 3D linear elasticity -- 4.1.7 The plane stress model -- 4.1.8 The plane strain model -- 4.2 The Stokes Problem -- 4.2.1 Divergence-free approximations -- 4.2.2 Approximations with nonzero divergence -- 4.2.3 Stokes problem in rotating system -- 4.3 A simple Maxwell type problem -- 4.3.1 Estimates of deviations from exact solutions -- 4.3.2 Numerical examples -- 4.4 Generalizations -- 4.4.1 Error majorant -- 4.4.2 Error minorant -- 5 Errors Generated By Uncertain Data -- 5.1 Mathematical models with incompletely known data -- 5.2 The accuracy limit -- 5.3 Estimates of the worst and best case scenario errors -- 5.4 Two-sided bounds of the radius of the solution set -- 5.5 Computable estimates of the radius of the solution set -- 5.5.1 Using the majorant -- 5.5.2 Using a reference solution -- 5.5.3 An advanced lower bound -- 5.6 Multiple sources of indeterminacy -- 5.6.1 Incompletely known right-hand side -- 5.6.2 The reaction diffusion problem -- 5.7 Error indication and indeterminate data -- 5.8 Linear elasticity with incompletely known Poisson ratio -- 5.8.1 Sensitivity of the energy functional -- 5.8.2 Example: axisymmetric model -- 6 Overview Of Other Results And Open Problems -- 6.1 Error estimates for approximations violating conformity -- 6.2 Linear elliptic equations -- 6.3 Time-dependent problems -- 6.4 Optimal control and inverse problems -- 6.5 Nonlinear boundary value problems -- 6.5.1 Variational inequalities -- 6.5.2 Elastoplasticity -- 6.5.3 Problems with power growth energy functionals -- 6.6 Modeling errors -- 6.7 Error bounds for iteration methods -- 6.7.1 General iteration algorithm -- 6.7.2 A priori estimates of errors -- 6.7.3 A posteriori estimates of errors -- 6.7.4 Advanced forms of error bounds -- 6.7.5 Systems of linear simultaneous equations -- 6.7.6 Ordinary differential equations -- 6.8 Roundoff errors -- 6.9 Open problems -- A Mathematical Background -- A.1 Vectors and tensors -- A.2 Spaces of functions -- A.2.1 Lebesgue and Sobolev spaces -- A.2.2 Boundary traces -- A.2.3 Linear functionals -- A.3 Inequalities -- A.3.1 The Hölder inequality -- A.3.2 The Poincaré and Friedrichs inequalities -- A.3.3 Korn’s inequality -- A.3.4 LBB inequality -- A.4 Convex functionals -- B Boundary Value Problems -- B.1 Generalized solutions of boundary value problems -- B.2 Variational statements of elliptic boundary value problems -- B.3 Saddle point statements of elliptic boundary value problems -- B.3.1 Introduction to the theory of saddle points -- B.3.2 Saddle point statements of linear elliptic problems -- B.3.3 Saddle point statements of nonlinear variational problems -- B.4 Numerical methods -- B.4.1 Finite difference methods -- B.4.2 Variational difference methods -- B.4.3 Petrov–Galerkin methods -- B.4.4 Mixed finite element methods -- B.4.5 Trefftz methods -- B.4.6 Finite volume methods -- B.4.7 Discontinuous Galerkin methods -- B.4.8 Fictitious domain methods -- C A Priori Verification Of Accuracy -- C.1 Projection error estimate -- C.2 Interpolation theory in Sobolev spaces -- C.3 A priori convergence rate estimates -- C.4 A priori error estimates for mixed FEM -- References -- Notation -- Index. |
| Record Nr. | UNINA-9910299716903321 |
Mali Olli
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| Dordrecht, Netherlands : , : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Verification and validation of 3D free-surface flow models [[electronic resource] /] / sponsored by Task Committee on 3D Free-Surface Flow Model Verification and Validation, Environmental and Water Resources Institute (EWRI) of the American Society of Civil Engineers ; edited by Sam S.Y. Wang ... [et al.]
| Verification and validation of 3D free-surface flow models [[electronic resource] /] / sponsored by Task Committee on 3D Free-Surface Flow Model Verification and Validation, Environmental and Water Resources Institute (EWRI) of the American Society of Civil Engineers ; edited by Sam S.Y. Wang ... [et al.] |
| Pubbl/distr/stampa | Reston, Va., : American Society of Civil Engineers, : EWRI, c2009 |
| Descrizione fisica | 1 online resource (503 p.) |
| Disciplina | 620.1/064015118 |
| Altri autori (Persone) | WangS. Y |
| Soggetto topico |
Fluid dynamics - Mathematical models
Numerical calculations - Verification |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-7844-7215-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1 Verification and Validation of Free Surface Flow Models""; ""1.1 Introduction""; ""1.2 Modeling of Physical Systems""; ""1.3 Free Surface Flow Numerical Model Development""; ""1.4 Verification and Validation""; ""1.5 Outline of a Systematic Model Verification and Validation Procedure""; ""1.6 Other Issues of Importance""; ""1.7 Findings, Conclusions, Recommendations and Input Data""; ""1.8 Request for Feedback""; ""1.9 References""; ""Chapter 2 Terminology and Basic Methodology""; ""2.1 Introduction""; ""2.2 Semantics""
""2.3 Code Verification and Validation: Numerical vs. Conceptual Modeling""""2.4 Code Confirmation""; ""2.5 Benchmarks and Inter-Code Comparisons""; ""2.6 Code Certification, Quality Assurance, and Accreditation""; ""2.7 Verification of Calculations""; ""2.8 Estimation of Uncertainty""; ""2.9 Grid Convergence vs. Iterative Convergence""; ""2.10 Error Taxonomies""; ""2.11 Truncation Error vs. Discretization Error""; ""2.12 Calibration and Tuning""; ""2.13 Software and Codes""; ""2.14 Code Options""; ""2.15 Zonal Verification""; ""2.16 Etymology and Near-Synonyms"" ""2.17 Limitations of Semantic Distinctions""""2.18 Basic Methodology of Calculation Verification""; ""2.19 References""; ""Chapter 3 Analytical Solutions for Mathematical Verification""; ""3.1 Introduction""; ""3.2 Test Case 1: Free-Surface Seiching in a Closed Rectangular Basin with Horizontal Bottom""; ""3.3 Test Case 2: Free-Surface Seiching in a Closed Circular Basin with a Horizontal Bottom""; ""3.4 Test Case 3: Tidal Forcing in a Rectangular Basin with a Horizontal Bottom""; ""3.5 Test Case 4: Tidal Forcing in a Rectangular Basin with a Varying Bottom Slope and Linear Bottom Friction"" ""3.6 Test Case 5: Wind-Driven Flow in a Closed Rectangular Basin with a Horizontal Bottom""""3.7 Test Case 6: Internal-Wave Seiching in a Rectangular Basin with a Horizontal Bottom""; ""3.8 Test Case 7: Density-Driven Flow in a Rectangular Basin with a Horizontal Bottom""; ""3.9 Test Case 8: A Three-Step Procedure to Check Nonlinear Effects from Tidal Circulation in a Square Basin with a Horizontal Bottom""; ""Chapter 4 Mathematical Verification Using Prescribed or Manufactured Solutions""; ""4.1 Introduction""; ""4.2 Method of Prescribed Solution Forcing (PSF)"" ""4.3 Method of Manufactured Solution (MMS)""""4.4 Model Verification Procedure of MMS""; ""4.5 Concluding Remarks""; ""4.6 References""; ""Chapter 5 Physical Process Validation""; ""5.1 Introduction""; ""5.2 Overview of Tests Cases""; ""5.3 Free Overfall Flow Test Case""; ""5.4 Delft U-Shaped Channel Flow (Indoor) Test Case""; ""5.5 Riprap Test Facility (Outdoor) Test Case""; ""5.6 Flow in a Channel with a Spur Dike Test Case""; ""5.7 Flow Around a Submerged Trapezoidal Spur Dike Test Case""; ""5.8 Flows Around a Groyne and in Harbor""; ""Chapter 6 Application Site Validation"" ""6.1 Introduction"" |
| Record Nr. | UNINA-9910458455903321 |
| Reston, Va., : American Society of Civil Engineers, : EWRI, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
